Local acceleration in fluid-flow situations exists only when
A flownet is a graphical representation of streamlines and equipotential lines such that
A free vortex
Stream lines, streak lines and path lines are all identical in case of
In irrotational flow of an ideal fluid
Match List-I (Format of representation) with List-ll (Context/Relevant to) and select the correct answer using the codes given below the lists:
1. Relevant to a velocity potential
2. Rate of rotation about a relevant axis
3. Pressure gradient in a relevant direction
4. Continuity of flow
A two-dimensional flow is described by velocity components u = 2x and v = - 2y. The discharge between points (1,1) and (2, 2) is equal to
Integrating (i), we get,
Differentiating (iii) w.r.t. y, we get,
Equating (ii) and (iv), we get,
f'(y) = 0 ....... (v)
Integrating (v), we get,
f(y) = C
where C is a numerical constant which can be treated as zero.
From (iii),. we get,
Consider the following statements in respect of two-dimensional incompressible flow with velocity components u and v in x and y directions respectively:
1. The continuity equation is
2. The acceleration in x-direction is
3. The condition of irrotationality is
4. The equation of a streamline is udy = -vdx
Which of these statements are correct?
For two dimensional incompressible flow, :
(i) the continuity equation is'
(ii) the equation of a stream line is vdx - udy = 0
An imaginary tangent at a point which shows the direction of velocity of a liquid particle at that point is
A path-line may be defined as the line traced by a single fluid particle as it moves over a period of time, Thus a path-line will show the direction of velocity of the same fluid particle at successive instants of time. As indicated earlier a streamline on the other hand shows the direction of velocity of a number of fluid particles at the same instant of time. A fluid particle always moves tangentially to the streamline, and in the case of steady flow since there is no change in direction of the velocity vector at any point with time, the streamline is fixed in space. Therefore in steady flow the pathlines and streamlines are identical. However, in unsteady flow since the direction of velocity vector at any point may change with time, streamline may shift in space from instant to instant. A particle then follows one streamline at one instant and another at the next instant and so on, so that the path of the particle may have no resemblance to any given instantaneous streamline. In other words, in unsteady flow path-lines and streamlines are different.
A two dimensional flow field is given by stream function ψ = x2 - y2. The magnitude of absolute velocity at a point (1, 1) is
at (1, 1) Vx = -2 m/s = Vy